Mixed-integer programming techniques for the scheduling of fuel oil and asphalt production

The objective of this paper is the development, solution and computational performance evaluation of mixed-integer programming (MIP) models of a real-world fuel oil and asphalt production scheduling problem at the PETROBRAS REVAP Refinery, which processes approximately 80% of all fuel oil consumed in Brazil. Two MIP models are proposed to define the optimal production policy, inventory control and distribution throughout a scheduling horizon of 3 days regarding the foreseen product demands under operational restrictions, with the objective of minimizing the operating cost. The problem is first modeled as a non-convex mixed-integer non-linear program (MINLP). A rigorous mixed-integer linear programming (MILP) model derived from the MINLP is then proposed. This linearization causes an increase in the model size; nevertheless it may theoretically be solved to global optimality. Additional modeling that considers transition costs due to undesirable mixing among products in pipelines is also proposed. The computational performances of both MIP models are evaluated and compared through real-world examples according to algorithmic structures and modeling features. The smaller model (MINLP), in which time horizon is uniformly discretized in 2h intervals, has 2629 continuous variables, 1512 0-1 variables and 4514 constraints. Results show that computational requirements of the proposed MIP models are similar and able to generate good solutions that are of practical relevance.